let T:R^2 to R^2 be linear operator given by formula T(x,y)=(2x-y,-8x+4y) then which of the following vectors are in kernal(T)
a)(5,10)
b)(3,2)
c)(1,1)

Question

let T:R^2 to R^2 be linear operator given by formula T(x,y)=(2x-y,-8x+4y) then which of the following vectors are in kernal(T)
a)(5,10)  
b)(3,2)
c)(1,1)

nikita2 · Answer

a

myininaya · Answer

its because T(5,10)=(0,0)
right?! :)

anonymous · Answer

if a vector, say v, is in the kernal(T), then that means T(v) = 0, so lets plug in the vectors and see which one comes out to 0:
T(5,10) = (2(5)-10, -8(5)+4(10)) = (10-10, -40+40) = (0,0)
wow thats luck lol, its a.

anonymous · Answer

on a side note, i dont like calling it the Kernal, i like calling it the Null Space.  Sounds much more awesome lol

anonymous · Answer

thank you sir i got the answer